ing-exercise-python/ex4.py at main · spechtnathan/ing-exercise-python · GitHub

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from matplotlib import pyplot
import numpy as np
import math


class Ex4:
    def __init__(self):
        self.message = "Exercice 4 initialized"
        print(self.message)

    def run(self):
        print("Running Exercice 4...")
        self.hermite(4, 2)
        x_values = np.linspace(-2, 2, 100)
        y_valuesH0 = [self.hermite(0, x) for x in x_values]
        y_valuesH1 = [self.hermite(1, x) for x in x_values]
        y_valuesH2 = [self.hermite(2, x) for x in x_values]
        y_valuesH3 = [self.hermite(3, x) for x in x_values]
        pyplot.plot(x_values, y_valuesH0, 'r')
        pyplot.plot(x_values, y_valuesH1, 'b')
        pyplot.plot(x_values, y_valuesH2, 'g')
        pyplot.plot(x_values, y_valuesH3, 'y')
        pyplot.title("Hermite Polynomials")
        pyplot.xlabel("x")
        pyplot.ylabel("H_n(x)")
        pyplot.legend(["H0", "H1", "H2", "H3"])
        pyplot.grid()
        pyplot.show()


    def hermite(self, n, x):
        H = 0
        for k in range(int(np.floor(n/2) + 1)):
            term = (-1)**k * math.factorial(n) / ( 2**k * math.factorial(k) * math.factorial(n - 2*k)) * x ** (n - 2*k)
            H += term
        return H